LEADER 05562nam 2200745Ia 450 001 9911019486103321 005 20200520144314.0 010 $a9786612307805 010 $a9781282307803 010 $a1282307800 010 $a9780470316979 010 $a0470316977 010 $a9780470317815 010 $a0470317817 035 $a(CKB)1000000000822228 035 $a(EBL)470285 035 $a(OCoLC)593219037 035 $a(SSID)ssj0000336750 035 $a(PQKBManifestationID)11223777 035 $a(PQKBTitleCode)TC0000336750 035 $a(PQKBWorkID)10283888 035 $a(PQKB)10886227 035 $a(MiAaPQ)EBC470285 035 $a(PPN)159326133 035 $a(Perlego)2757908 035 $a(EXLCZ)991000000000822228 100 $a19990615d2000 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDirectional statistics /$fKanti V. Mardia, Peter E. Jupp 205 $a[2nd ed.]. 210 $aChichester ;$aNew York $cWiley$dc2000 215 $a1 online resource (452 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 08$a9780471953333 311 08$a0471953334 320 $aIncludes bibliographical references and index. 327 $aDirectional Statistics; Contents; 11.1 INTRODIUCTION; Preface; 1 Circular Data; 1.1 INTRODUCTION; 1.2 DIAGR. AMMATICAL REPR.ESEXT.4TION; 1.2.1 Ungrouped Data; 1.2.2 Grouped Data; 1.2.3 Axial Data; 1.3 FORMS OF FREQUENCY DISTRIBUTIOSS; 1.3.1 Unimodal Distributions; 1.3.2 Multimodal Distributions; 1.4 FRTHER EXAMPLES OF DIRECTINAL DATA; 1.4.1 Earth Sciences; 1.4.2 Meteorology; 1.4.3 Biology; 1.4.4 Physics; 1.4.5 Psychology; 1.4.6 Image Analysis; 1.4.7 Medicine; 1.4.8 Astronomy; 1.5 Wrapping and Projecting; 2 Summary Statistics; 2.1. INTRODUCTION; 2.1.1 Preliminaries and Notation 327 $a2.2 MEASUCRES OF LOCATION2.2.1 The Mean Direction; 2.2.2 The Metiiari Direr:tion; 2.3 MEASUR.ES OF CONCENTRATIOX AND DISPERSION; 2.3.1 The Mean Rwultant Length arid the Circular Variance; 2.3.2 Dworriposit.ion of Dispersion; 2.3.3 The Circirlw Standard Deviation; 2.3.4 Other M(xmres of Dispersion; 2.4 TRIGONOMETRIC I\IIOMEXTS; 2.4.1 Defiuitions; 2.4.2 Measures of Skewness mid Kurtosis; 2.5 CORRECTIOKS FOR GROUPING; 3 Basic Concepts and Models; 3.1 INTRODUCTIOS; 3.2 THE DISTRIBUTIORT FUNCTIOIV; 3.3 THE CHARACTERISTlC FUXCTIOX; 3.3.1 Definition; 3.3.2 Fourier Series 327 $a3.3.3 Indepeiidence and Convolution3.4 MOMESTS AND MEASURES OF LOCATION AND DISPERSIOS; 3.4.1 Trigonometric Moments; 3.4.2 Measures of Loration arid Dispersion; 3.4.3 A Chebysheu Inequality; 3.4.4 Symmetrical Dist.ribut.ions; 3.5 CIRCULAR MODELS; 3.5.1 Introduction; 3.5.2 Lattice Distributions; 3.5.3 Uniform Distribution; 3.5.4 Von Mises Distributions; 3.5.5 Carciioid Distributions; 3.5.6 Projwtrd Normal Distributions; 3.5.7 Wrapped Distributions; 3.6 MULTIPLY-WRAPPED DISTRIBUTIONS; 3.6.1 Wrapping the Circle rmtct Itself; 3.6.2 Mixtures; 3.7 DISTRIBUTIOKS ON THE TORUS AND THE CYLINDER 327 $a3.7.1 Distributions on the Torus3.7.2 Distributions on the CyliIidrr; 4 Fundamental Theorems and Distribution Theory; 4.1 INTRODCCTION; 4.2 PROPERTIES OF CHARACTERISTIC FUNCTIOKS; 4.2.1 Key Properties; 4.2.2 Polnr Distributions mid Characteristic. FuIictions; 4.2.3 Further Properties of the Chwactcristir: Function; 4.3 LIMIT THEOREMS; 4.3.1 Central Linlit Theorems; 4.3.2 Poincar6's Theorem; 4.4 THE DISTRIBUTION OF # AND R FROM THE UNIFORM DISTRIBUTION; 4.4.1 The Distribution of 8 md R; 4.4.2 The Distribution of C and S; 4.5 DISTRIBUTION OF C, S AND R FOR A VON MISES POPLLATIOX 327 $a4.5.1 The Joint Distribution of C and S4.5.2 Distributions of 8 and .; 4.5.3 hifarginal Distributions of C and S; 4.6 PROBLE~iFORVON~,~SESPOPUL.4TIOSS 4.6 DISTRIBUTIONS RELATED TO THE MULTI-SAhIPLE; 4.6.1 The Distribution of R; 4.6.2 The Joint Distribution of' (R, R); 4.6.3 Distributions for the Homogeneous Case; 4.7 MOMENTS OF R; 4.8 LIMITING DISTRIBUTIONS OF CIRCULAR . STATISTICS; 4.8.1 Large-Sample Approximations; 4.8.2 High-Concentration Approximations; 4.8.3 Furthtr Approximations to the Distribution of R; 5 Point Estimation; 5.1 INTRODUCTION 327 $a5.2 UNBIASED ESTIMATORS AND A CRAMER-RAO BOUND 330 $aPresents new and up-dated material on both the underlying theory and the practical methodology of directional statistics, helping the reader to utilise and develop the techniques appropriate to their work.The book is divided into three parts. The first part concentrates on statistics on the circle. Topics covered include tests of uniformity, tests of good-of-fit, inference on von Mises distributions and non-parametric methods. The second part considers statistics on spheres of arbitrary dimension, and includes a detailed account of inference on the main distributions on spheres. Recent mat 410 0$aWiley series in probability and statistics. 606 $aDistribution (Probability theory) 606 $aMathematical statistics 606 $aSampling (Statistics) 615 0$aDistribution (Probability theory) 615 0$aMathematical statistics. 615 0$aSampling (Statistics) 676 $a519.5 700 $aMardia$b K. V$012429 701 $aJupp$b Peter E$055995 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019486103321 996 $aDirectional statistics$9104121 997 $aUNINA